Research
Bayesian inference in classical lattices and MIPT
We explore the Bayesian measurement problem in different lattice models, mainly the Ising model in \(6-\epsilon\) dimensions and \(2\)-dimensions. We uncover an enlarged/emergent symmetry similar to the one seen along the Nishimori line.
arXiv:2604.23346, with Prof. Kay Wiese and Prof. Adam NahumIsing model on Hyperbolic lattices
Using a dual construction and employing a recently developed automorphic Bloch theorem for non-abelian Fuchsian groups, we analytically study the free fermionic spectrum of the Ising model for some specific hyperbolic lattices. From this, we try to understand their various properties in the intermediate phase between two transitions. (with Prof. Kedar Damle, Manuscript under preparation)
Free Fermionic Representation of Random Bond Ising Model
In this work, we construct a general dual mapping of the random bond Ising model for arbitrary planar graphs. We explain this dual fermionic Hamiltonian's disorder-induced low-energy (LE) modes using a novel mapping of frustration to isolated sites (say monomers) and their mixing. We give a bound on the quenched-averaged CDF of this LE mode and try to get a better understanding of the Griffith's phase. Furthermore, we investigate the fluctuation of the free energy density along this line using these modes. (with Prof. Kedar Damle, Manuscript under preparation).